The Hammers' season appeared to turn a corner last week when they beat Newcastle, but they were then thrashed 5-2 by Arsenal on Saturday.
West Ham have four wins from 13 Premier League matches and are 14th in the standings, eight points outside of the European spots.
Lopetegui has not been able to make them a competitive side and there is growing pressure on him to improve their results.
However, if West Ham decide to make a change, Conceicao could be in contention for the job at the London Stadium.
Conceicao left Porto in June following a seven-year spell in which he won the Portuguese league title on three occasions.
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The 50-year-old, previously of Olhanense, Academica, Braga, Vitoria Guimaraes and Nantes, also has Champions League experience.
West Ham technical director Tim Steidten is understood to be a huge fan of Conceicao.
talkSPORT reported last month that he has become of interest to West Ham and other sides in the Premier League who may wish to change manager.
Conceicao is the latest name linked as a potential replacement for Lopetegui, who replaced David Moyes in the summer.
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Former Borussia Dortmund boss Edin Terzic has been sounded out by West Ham and is admired by club chief Steidten.
Terzic has past experience with the Hammers as he was an assistant coach to Slaven Bilic during his tenure from 2015 to 2017.
West Ham's defeat to Arsenal was the sixth match in all competitions this season that they have conceded at least three goals.
Opposition sides have scored against them 24 times in the Premier League alone and they have a goal difference of minus seven.
Although their current league standing makes for disappointing reading, upcoming fixtures offer great chances to climb the table.
They first travel to 16th-place Leicester City, who recently appointed Ruud van Nistelrooy as manager, on Tuesday night.
West Ham then return home this weekend to face a Wolves side who are in the relegation zone and have won only twice.
Bournemouth and Brighton will emerge as tough tests before they come up against bottom-of-the-table Southampton.